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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Equation of Pair of Straight Lines

  • question_answer
    If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]represents a pair of lines then \[a=\] [Karnataka CET  2004]

    A)            - 16                                           

    B)            16

    C)            4    

    D)            - 4

    Correct Answer: B

    Solution :

               Given equation is \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]            Here \[A=a,B=-1,\,H=0,\,G=2,F=\frac{-1}{2},\,C=0\]            If the given equation represents a pair of straight lines, then \[ABC+2FGH-A{{F}^{2}}-B{{G}^{2}}-C{{H}^{2}}=0\]            \[0-0-a\,\left( \frac{1}{4} \right)-(-1)(4)=0\] Þ \[\frac{-a}{4}=4=0\Rightarrow a=16\].


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